Table 2.

Variable screening and selection for models considered in simulation studies for a binary confounder $L_i\in \{0,1\}$

Model	Variables screened	Maximum model size
Conditional Std	$\{{\beta }_1^l,\cdots ,{\beta }_p^l\}$ (independently $\forall l$)	$d_l=\lfloor n_l/log(n_l)\rfloor$ $\forall l$
Select L	$\{{\beta }_1,\cdots ,{\beta }_p,L\}$	$d=\lfloor n/log(n)\rfloor$
Select L EffMod	$\{{\beta }_1^{l=0},\cdots ,{\beta }_p^{l=0},{\beta }_1^{l=1},\cdots ,{\beta }_p^{l=1},L\}$	$d=\lfloor n/log(n)\rfloor$
Require L	$\{{\beta }_1,\cdots ,{\beta }_p\}$ (given L)	$d=\lfloor n/log(n)\rfloor$
Require L EffMod	$\{{\beta }_1^{l=0},\cdots ,{\beta }_p^{l=0},{\beta }_1^{l=1},\cdots ,{\beta }_p^{l=1}\}$ (given L)	$d=\lfloor n/log(n)\rfloor$
Ignore L	$\{{\beta }_1,\cdots ,{\beta }_p\}$	$d=\lfloor n/log(n)\rfloor$
Ignore L EffMod	$\{{\beta }_1^{l=0},\cdots ,{\beta }_p^{l=0},{\beta }_1^{l=1},\cdots ,{\beta }_p^{l=1}\}$	$d=\lfloor n/log(n)\rfloor$